2v^2-12v+18=162

Solution for 2v^2-12v+18=162 equation:

Simplifying
2v2 + -12v + 18 = 162

Reorder the terms:
18 + -12v + 2v2 = 162

Solving
18 + -12v + 2v2 = 162

Solving for variable 'v'.

Reorder the terms:
18 + -162 + -12v + 2v2 = 162 + -162

Combine like terms: 18 + -162 = -144
-144 + -12v + 2v2 = 162 + -162

Combine like terms: 162 + -162 = 0
-144 + -12v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -6v + v2) = 0

Factor a trinomial.
2((-6 + -1v)(12 + -1v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(12 + -1v)' equal to zero and attempt to solve:

Simplifying
12 + -1v = 0

Solving
12 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1v = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1v = 0 + -12
-1v = 0 + -12

Combine like terms: 0 + -12 = -12
-1v = -12

Divide each side by '-1'.
v = 12

Simplifying
v = 12
Solution
v = {-6, 12}